In this study, a systematic approach is presented for the stress analysis of shell intersections made of composite materials. The finite element method used is based on a modified mixed formulation and two-dimensional laminated shell theory. The calculation algorithm and capabilities of the specialpurpose computer program SAIS are discussed. The numerical and the experimental results are compared. A parametric study of intersecting composite laminated cylindrical shells was performed. The numerical results presented show the effects of specific properties of composite materials on stresses in shell intersections under internal pressure loading.